The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility II: An Artificial Market Generator

ArXiv ID: 2509.05065 “View on arXiv”

Authors: Guillaume Maitrier, Grégoire Loeper, Jean-Philippe Bouchaud

Abstract

This work extends and complements our previous theoretical paper on the subtle interplay between impact, order flow and volatility. In the present paper, we generate synthetic market data following the specification of that paper and show that the approximations made there are actually justified, which provides quantitative support our conclusion that price volatility can be fully explained by the superposition of correlated metaorders which all impact prices, on average, as a square-root of executed volume. One of the most striking predictions of our model is the structure of the correlation between generalized order flow and returns, which is observed empirically and reproduced using our synthetic market generator. Furthermore, we were able to construct proxy metaorders from our simulated order flow that reproduce the square-root law of market impact, lending further credence to the proposal made in Ref. [“2”] to measure the impact of real metaorders from tape data (i.e. anonymized trades), which was long thought to be impossible.

Keywords: Market Impact, Square-Root Law, Order Flow, Volatility Modeling, Metaorders, Equities

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 7.2/10
• Quadrant: Holy Grail
• Why: The paper presents dense mathematical derivations and complex theoretical models (generalized propagator, power-law scaling, correlation exponents), justifying a high math score. It also details a specific artificial market simulation with parameter fitting and synthetic data generation, showing strong empirical implementation, though it remains a simulation rather than live trading.

  flowchart TD
    A["Research Goal:<br>Quantify the interplay between<br>market impact, order imbalance, and volatility"] --> B["Data/Input:<br>Theoretical model from<br>companion paper"]
    B --> C["Methodology:<br>Agent-Based / Artificial Market<br>Generator"]
    C --> D["Computational Process:<br>Simulate synthetic order flow<br>and price formation"]
    D --> E{"Analysis & Validation"}
    E --> F["Outcome 1:<br>Approximations justified:<br>Volatility explained by<br>correlated metaorder superposition"]
    E --> G["Outcome 2:<br>Synthetic order flow reproduces<br>empirical correlation structure"]
    E --> H["Outcome 3:<br>Proxy metaorders confirm<br>Square-Root Impact Law"]